Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
220 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #22549681 | C2 | semidirect |
| 5. #22549680 | C2 | semidirect |
| 6. #22549679 | C2 | semidirect |
| 7. #358×C127 | C2 | semidirect |
| 12. Q16×D127 | C4 | semidirect |
| 78. C127 | #2141 | semidirect |
| 85. #358 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D127 | 2 |
| C2×#16861148 | 2 |
| #22549913 | 2 |
| #22549681 | 2 |
| #22549680 | 2 |
| #22549679 | 2 |
| #358×C127 | 2 |
| #2141 | 127 |